Abstract
This paper discusses about a two stage queueing system with shared server and the delay time between two end to end responses. This system is examined as almost the process of quasi-birth and death and the necessary and sufficient conditions for system stability are discussed. The ErntPS algorithm for VoIP Services has recently been investigated for average delay in queueing and it has been proven that ErtPS can allow more users than UGS. However, we need the distribution of probabilities of queue delays in order to include information necessary for QoS rather than the average queue delays. Some fascinating performance measures are achieved by matrix geometric method. The server wishes to determine the optimal point of differentiation and its optimal buffer size. Finally we find the delay time differentiation and the specific probabilistic system descriptors.
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